149 citations · 841 across the 44 of their papers we have counts for
3 papers · 2 filters
Mixing time and eigenvalues of the abelian sandpile Markov chain
Daniel C. Jerison, Lionel Levine, John Pike
The abelian sandpile model defines a Markov chain whose states are integer-valued functions on the vertices of a simple connected graph . By viewing this chain as a (nonreversib…
Formation of an interface by competitive erosion
Shirshendu Ganguly, Lionel Levine, Yuval Peres +1
In 2006, the fourth author proposed a graph-theoretic model of interface dynamics called competitive erosion. Each vertex of the graph is occupied by a particle that can be either…
The divisible sandpile at critical density
Lionel Levine, Mathav Murugan, Yuval Peres +1
The divisible sandpile starts with i.i.d. random variables ("masses") at the vertices of an infinite, vertex-transitive graph, and redistributes mass by a local toppling rule in an…